Volume of a square using cross section

In summary, the problem involves finding the volume of the area bounded by two curves where the cross sections are perpendicular to the y-axis. The solution will involve taking an integral with respect to y, rather than x.
  • #1
mikaloveskero
6
0

Homework Statement


What is the volume if the area bounded by y=x^2 and y=9 and the cross sections are perpendicular to the y axis


Homework Equations





The Attempt at a Solution


I have no idea
 
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  • #2
At least draw the graph and make an attempt. Take a picture of it or scan it or just draw it in some picture editor and attach it to your post.
 
  • #3
I drew the picture and y=9 is the higher graph and y=x^2 is the lower graph. So from there do you do (9-x^2)^2 and take the integral from -3 to 3 ?
 
  • #4
The cross sections are perpendicular to the y-axis, not parallel. So the integral will be with respect to y, not x.
 

FAQ: Volume of a square using cross section

What is the formula for finding the volume of a square using cross section?

The formula for finding the volume of a square using cross section is V = A * h, where V is the volume, A is the area of the square, and h is the height of the cross section.

Can the volume of a square using cross section be calculated if the cross section is not a perfect square?

Yes, the volume can still be calculated as long as the cross section has a known area and the height is perpendicular to the base of the square.

How does the volume of a square using cross section differ from the volume of a regular square?

The volume of a regular square is calculated by multiplying the length, width, and height, while the volume of a square using cross section is calculated by multiplying the area of the square and the height of the cross section.

Can the volume of a square using cross section be negative?

No, the volume cannot be negative as it is a measure of space and cannot have a negative value.

Are there any real-world applications of calculating the volume of a square using cross section?

Yes, this concept is commonly used in construction to calculate the volume of objects with a square base, such as buildings or containers. It is also used in engineering and manufacturing to determine the volume of square-shaped objects.

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